Time to dig out that old thinking cap, dust it off, and put it on.
They are talking about international flights (AA) connecting to domestic flights (B6). It appears to say that you will be able to earn AA miles on AA's flights, and B6 miles on B6's flights. At least, that's how I interpret the word
respectively.
But now that
AmericanAirlines is taking a deeper role in Flyertalk, adding to our conversations, perhaps he will comment. Where is that darn BatSignal when we need it?